#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# Copyright (C) 2016-2020 Stephane Caron <stephane.caron@normalesup.org>
#
# This file is part of qpsolvers.
#
# qpsolvers is free software: you can redistribute it and/or modify it under
# the terms of the GNU Lesser General Public License as published by the Free
# Software Foundation, either version 3 of the License, or (at your option) any
# later version.
#
# qpsolvers is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
# A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
# details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with qpsolvers. If not, see <http://www.gnu.org/licenses/>.
from cvxopt import matrix, spmatrix
from cvxopt.solvers import options, qp
from numpy import array, ndarray
options['show_progress'] = False # disable cvxopt output
def cvxopt_matrix(M):
"""
Convert matrix to CVXOPT format.
Parameters
----------
M : numpy.array
Matrix in NumPy format.
Returns
-------
N : cvxopt.matrix
Matrix in CVXOPT format.
"""
if type(M) is ndarray:
return matrix(M)
elif type(M) is spmatrix or type(M) is matrix:
return M
coo = M.tocoo()
return spmatrix(
coo.data.tolist(), coo.row.tolist(), coo.col.tolist(), size=M.shape)
def cvxopt_solve_qp(P, q, G=None, h=None, A=None, b=None, solver=None,
initvals=None, verbose=False):
"""
Solve a Quadratic Program defined as:
.. math::
\\begin{split}\\begin{array}{ll}
\\mbox{minimize} &
\\frac{1}{2} x^T P x + q^T x \\\\
\\mbox{subject to}
& G x \\leq h \\\\
& A x = h
\\end{array}\\end{split}
using `CVXOPT <http://cvxopt.org/>`_.
Parameters
----------
P : numpy.array, cvxopt.matrix or cvxopt.spmatrix
Symmetric quadratic-cost matrix.
q : numpy.array, cvxopt.matrix or cvxopt.spmatrix
Quadratic-cost vector.
G : numpy.array, cvxopt.matrix or cvxopt.spmatrix
Linear inequality matrix.
h : numpy.array, cvxopt.matrix or cvxopt.spmatrix
Linear inequality vector.
A : numpy.array, cvxopt.matrix or cvxopt.spmatrix
Linear equality constraint matrix.
b : numpy.array, cvxopt.matrix or cvxopt.spmatrix
Linear equality constraint vector.
solver : string, optional
Set to 'mosek' to run MOSEK rather than CVXOPT.
initvals : numpy.array, optional
Warm-start guess vector.
verbose : bool, optional
Set to `True` to print out extra information.
Returns
-------
x : array, shape=(n,)
Solution to the QP, if found, otherwise ``None``.
Note
----
CVXOPT only considers the lower entries of `P`, therefore it will use a
wrong cost function if a non-symmetric matrix is provided.
"""
options['show_progress'] = verbose
args = [cvxopt_matrix(P), cvxopt_matrix(q)]
kwargs = {'G': None, 'h': None, 'A': None, 'b': None}
if G is not None:
kwargs['G'] = cvxopt_matrix(G)
kwargs['h'] = cvxopt_matrix(h)
if A is not None:
kwargs['A'] = cvxopt_matrix(A)
kwargs['b'] = cvxopt_matrix(b)
sol = qp(*args, solver=solver, initvals=initvals, **kwargs)
if 'optimal' not in sol['status']:
return None
return array(sol['x']).reshape((q.shape[0],))
